For each of the following changes in operating condition for a dc shunt motor, describe how the armature current and speed will vary:

a. Halving the armature terminal voltage while the field fluxes and load torque remain constant.

b. Halving the armature terminal voltage while the field current and load power remain constant.

c. Doubling the field flux while the armature terminal voltage and load torque remain constant.

d. Halving both the field flux and armature terminal voltage while the load power remains constant.

e. Halving the armature terminal voltage while the field flux remains constant and the load torque varies as the square of the speed. Only brief quantitative statements describing the general nature of the effect are required, for example, "speed approximately doubled."